\documentclass[]{article}
\usepackage{amsmath,tkz-linknodes}
\usepackage{stmaryrd}
\usepackage{tikz}

%\usepackage[graphics,tightpage,active]{preview}
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\newlength{\imagewidth}
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\input{common}

\begin{document}
\thispagestyle{empty}
\begin{NodesList}[margin=3cm]
\begin{align*}
  \alpha [\neg \phi] & = \alpha \sqcap \sim{\alpha [\phi]}
  \AddNode \\
% \intertext{\hfil \ldots and since $\alpha = \alpha \wedge \alpha$\ldots  \hfil}
  & = (\alpha \sqcap \alpha) \sqcap \sim{\alpha [\phi]} \AddNode \\
% \intertext{\hfil \ldots by associativity \ldots \hfil }
  & = \alpha \sqcap (\alpha \sqcap \sim{\alpha [\phi]}) \AddNode \\
% \intertext{\hfil \ldots by commutativity \ldots \hfil }
%  & = \alpha \wedge ( \sim{\alpha [\phi]} \wedge \alpha) \AddNode \\
 % \intertext{ \hfil whence by definition, \hfil }
  & = \alpha \sqcap \alpha [\neg \phi] \AddNode
\end{align*}
 
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\LinkNodes{Since $\alpha = \alpha \sqcap \alpha$}%
\LinkNodes{Associativity }%
%\LinkNodes{ commutativity }%
\LinkNodes{By definition}
   \end{NodesList}
\end{document}